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Gamelismic clan: Difference between revisions

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The 2.3.7 [[Just_intonation_subgroups|subgroup]] comma for the gamelismic clan is the gamelisma, 1029/1024, with monzo |-10 1 0 3>. For any member of the clan, for the rank three [[Gamelismic_family#Gamelan|gamelan temperament]] itself, and for the rank two 2.3.7 temperament [[Slendric|slendric]], this means three 8/7 intervals give a fifth, 3/2. In fact, we find that 3/2 = (8/7)^3 * 1029/1024. From this it follows that gamelismic temperaments tend to flatten the both fifth and the 7/4, or if they do not, the other of the pair must be flattened even more. [[36edo]] is a good tuning for gamelismic itself, though if the full 7-limit is desired, [[72edo]], [[77edo]] or [[118edo]] might be preferred.
The 2.3.7 [[Just_intonation_subgroups|subgroup]] comma for the '''gamelismic clan''' is the gamelisma, [[1029/1024]], with monzo {{monzo|-10 1 0 3}}. For any member of the clan, for the rank three [[Gamelismic family #Gamelan|gamelan temperament]] itself, and for the rank two 2.3.7 temperament [[slendric]], this means three [[8/7]] intervals give a fifth, [[3/2]]. In fact, we find that 3/2 = (8/7)<sup>3</sup> × 1029/1024. From this it follows that gamelismic temperaments tend to flatten both the fifth and the 7/4, or if they do not, the other of the pair must be flattened even more. [[36edo]] is a good tuning for gamelismic itself, though if the full 7-limit is desired, [[72edo]], [[77edo]] or [[118edo]] might be preferred.


7-limit minimax
7-limit minimax
Line 21: Line 21:
Map to lattice: [&lt;0 3 0 -1|, &lt;0 0 1 0|]
Map to lattice: [&lt;0 3 0 -1|, &lt;0 0 1 0|]


Map: [&lt;1 1 0 3|, &lt;0 3 0 -1|, &lt; 0 0 1 0|]
No-five map: [&lt;1 1 0 3|, &lt;0 3 0 -1|]


Generators: 2, 5, 7
No-five mapping generators: 2, 8/7


No-fives [[POTE_tuning|POTE generator]]: 233.688
No-five [[POTE_tuning|POTE generator]]: ~8/7 = 233.688


EDOs: 5, 36, 77, 190
No-five EDOs: {{EDOs|5, 36, 77, 190}}


==Full seven limit children==
== Full seven limit children ==
To the gamelisma itself we need to add the comma which appears next on the modified [[Normal_lists|normal comma list]], which is often a 5-limit comma. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use 8/7 as a generator, though in the case of gidorah that's the same as 6/5. Miracle adds 33075/32768 and uses the secor, half an 8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of 21/20 and superkleismic adds 875/864 with a generator of 6/5. Unidec adds 4375/4374, and has a generator of 10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a major third. Finally, tritikleismic adds 15625/15536 and has a generator of 6/5 with a 1/3 octave period.
To the gamelisma itself we need to add the comma which appears next on the modified [[Normal_lists|normal comma list]], which is often a 5-limit comma. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use 8/7 as a generator, though in the case of gidorah that's the same as 6/5. Miracle adds 33075/32768 and uses the secor, half an 8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of 21/20 and superkleismic adds 875/864 with a generator of 6/5. Unidec adds 4375/4374, and has a generator of 10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a major third. Finally, tritikleismic adds 15625/15536 and has a generator of 6/5 with a 1/3 octave period.


=Miracle=
Discussed under their respective 5-limit family are [[Meantone family #Mothra|mothra]] and [[Schismatic family #Guiron|guiron]]. The rest are considered below.
 
= Miracle =
{{main|Miracle}}
 
[[Comma|Commas]]: 225/224, 1029/1024
[[Comma|Commas]]: 225/224, 1029/1024


Line 55: Line 59:
Wedgie: &lt;&lt;6 -7 -2 -25 -20 15||
Wedgie: &lt;&lt;6 -7 -2 -25 -20 15||


EDOs: 10, 21, 31, 41, 72, [[175edo|175]]
EDOs: {{EDOs|10, 21, 31, 41, 72, 175}}


Badness: 0.0167
Badness: 0.0167


==11-limit==
== 11-limit ==
[[Comma|Commas]]: 225/224, 243/242, 385/384
[[Comma|Commas]]: 225/224, 243/242, 385/384


Line 76: Line 80:
Map: [&lt;1 1 3 3 2|, &lt;0 6 -7 -2 15|]
Map: [&lt;1 1 3 3 2|, &lt;0 6 -7 -2 15|]


[[EDO|EDOs]]: 10, 31, 41, [[72edo|72]], 247c, 319bcde, [[391edo|391bcde]], 463bccde
[[EDO|EDOs]]: {{EDOs|10, 31, 41, 72, 247c, 319bcde, 391bcde, 463bccde}}


Badness: 0.0107
Badness: 0.0107


[[Chords_of_miracle|Chords of miracle]]
{{see also|Chords of miracle}}
 
==Revelation==
Commas: 99/98, 176/175, 1029/1024
 
POTE generator: ~15/14 = 116.277
 
Map: [&lt;1 1 3 3 5|, &lt;0 6 -7 -2 -16|]
 
EDOs: 10e, 21, 31


Badness: 0.0329
=== Miraculous ===
 
===13-limit===
Commas: 66/65, 99/98, 105/104, 512/507
 
POTE generator: ~15/14 = 116.268
 
Map: [&lt;1 1 3 3 5 4|, &lt;0 6 -7 -2 -16 -3|]
 
EDOs: 10e, 21, 31
 
Badness: 0.0295
 
==Miraculous==
Commas: 105/104, 144/143, 196/195, 243/242
Commas: 105/104, 144/143, 196/195, 243/242


Line 111: Line 93:
Map: [&lt;1 1 3 3 2 4|, &lt;0 6 -7 -2 15 -3|]
Map: [&lt;1 1 3 3 2 4|, &lt;0 6 -7 -2 15 -3|]


EDOs: 10, 31, 41, 72f, 113f, 185cff
EDOs: {{EDOs|10, 31, 41, 72f, 113f, 185cff}}


Badness: 0.0187
Badness: 0.0187


==Benediction==
=== Benediction ===
Commas: 225/224, 243/242, 351/350, 385 /384
Commas: 225/224, 243/242, 351/350, 385/384


POTE generator: ~15/14 = 116.574
POTE generator: ~15/14 = 116.574
Line 122: Line 104:
Map: [&lt;1 1 3 3 2 7|, &lt;0 6 -7 -2 15 -34|]
Map: [&lt;1 1 3 3 2 7|, &lt;0 6 -7 -2 15 -34|]


EDOs: 31, 72, 103, [[175edo|175f]]
EDOs: {{EDOs|31, 72, 103, 175f}}


Badness: 0.0157
Badness: 0.0157


===17-limit===
==== 17-limit ====
Commas: 225/224, 243/242, 273/272, 351/350, 375/374
Commas: 225/224, 243/242, 273/272, 351/350, 375/374


Line 133: Line 115:
Map: [&lt;1 1 3 3 2 7 7|, &lt;0 6 -7 -2 15 -34 -30|]
Map: [&lt;1 1 3 3 2 7 7|, &lt;0 6 -7 -2 15 -34 -30|]


EDOs: 31, 72, 103, 175f
EDOs: {{EDOs|31, 72, 103, 175f}}


==Manna==
=== Manna ===
Commas: 225/224, 243/242, 325/324, 385/384
Commas: 225/224, 243/242, 325/324, 385/384


Line 142: Line 124:
Map: [&lt;1 1 3 3 2 0|, &lt;0 6 -7 -2 15 38|]
Map: [&lt;1 1 3 3 2 0|, &lt;0 6 -7 -2 15 38|]


EDOs: 10f, 31f, 41, 72, 113, 185cf, 257cff
EDOs: {{EDOs|10f, 31f, 41, 72, 113, 185cf, 257cff}}


Badness: 0.0170
Badness: 0.0170


==Semimiracle==
=== Semimiracle ===
Commas: 169/168, 225/224, 243/242, 385/384
Commas: 169/168, 225/224, 243/242, 385/384


Line 153: Line 135:
Map: [&lt;2 2 6 6 4 7|, &lt;0 6 -7 -2 15 2|]
Map: [&lt;2 2 6 6 4 7|, &lt;0 6 -7 -2 15 2|]


EDOs: 10, 62, 72
EDOs: {{EDOs|10, 62, 72}}


Badness: 0.0246
Badness: 0.0246


===17-limit===
==== 17-limit ====
Commas: 169/168, 221/220, 225/224, 243/242, 273/272
Commas: 169/168, 221/220, 225/224, 243/242, 273/272


Line 164: Line 146:
Map: [&lt;2 2 6 6 4 7 7|, &lt;0 6 -7 -2 15 2 6|]
Map: [&lt;2 2 6 6 4 7 7|, &lt;0 6 -7 -2 15 2 6|]


EDOs: 10, 62, 72
EDOs: {{EDOs|10, 62, 72}}


Badness: 0.0161
Badness: 0.0161


==Hemimiracle==
=== Hemisecordite ===
Commas: 225/224, 245/242, 1029/1024
 
POTE generator: ~33/32 = 58.408
 
Map: [&lt;1 1 3 3 4|, &lt;0 12 -14 -4 -11|]
 
EDOs: 20, 21, 41, 144e, 185cee, 226cee
 
Badness: 0.0592
 
===13-limit===
Commas: 105/104, 196/195, 245/242, 512/507
 
POTE generator: ~33/32 = 58.430
 
Map: [&lt;1 1 3 3 4 4|, &lt;0 12 -14 -4 -11 -6|]
 
EDOs: 20, 21, 41, 144eff, 185ceeff
 
Badness: 0.0432
 
==Oracle==
Commas: 121/120, 225/224, 1029/1024
 
POTE generator: ~11/8 = 541.668
 
Map: [&lt;1 7 -4 1 3|, &lt;0 -12 14 4 1|]
 
EDOs: 11, 20, 31, 51, 82e, 113e, 144ee
 
Badness: 0.0427
 
==Hemisecordite==
Commas: 225/224, 243/242, 385/384, 847/845
Commas: 225/224, 243/242, 385/384, 847/845


Line 208: Line 157:
Map: [&lt;1 1 3 3 2 2|, &lt;0 12 -14 -4 30 35|]
Map: [&lt;1 1 3 3 2 2|, &lt;0 12 -14 -4 30 35|]


EDOs: 41, 62, 103, 247c, 350bcde
EDOs: {{EDOs|41, 62, 103, 247c, 350bcde}}


Badness: 0.0256
Badness: 0.0256


===17-limit===
==== 17-limit ====
Commas: 225/224, 243/242, 273/272, 385/384, 847/845
Commas: 225/224, 243/242, 273/272, 385/384, 847/845


Line 219: Line 168:
Map: [&lt;1 1 3 3 2 2 2|, &lt;0 12 -14 -4 30 35 43|]
Map: [&lt;1 1 3 3 2 2 2|, &lt;0 12 -14 -4 30 35 43|]


EDOs: 41, 62, 103
EDOs: {{EDOs|41, 62, 103}}


Badness: 0.0225
Badness: 0.0225


==Phicordial==
=== Phicordial ===
Commas: 225/224, 243/242, 385/384, 2200/2197
Commas: 225/224, 243/242, 385/384, 2200/2197


Line 230: Line 179:
Map: [&lt;1 7 -4 1 17 4|, &lt;0 -18 21 6 -45 -1|]
Map: [&lt;1 7 -4 1 17 4|, &lt;0 -18 21 6 -45 -1|]


EDOs: 10, 103, 113, 216c
EDOs: {{EDOs|10, 103, 113, 216c}}


Badness: 0.0332
Badness: 0.0332


===17-limit===
==== 17-limit ====
Commas: 225/224, 243/242, 273/272, 441/440, 2200/2197
Commas: 225/224, 243/242, 273/272, 441/440, 2200/2197


Line 241: Line 190:
Map: [&lt;1 7 -4 1 17 4 8|, &lt;0 -18 21 6 -45 -1 -13|]
Map: [&lt;1 7 -4 1 17 4 8|, &lt;0 -18 21 6 -45 -1 -13|]


EDOs: 10, 103, 113, 216c
EDOs: {{EDOs|10, 103, 113, 216c}}


Badness: 0.0247
Badness: 0.0247


==Music==
== Revelation ==
By [[Gene_Ward_Smith|Gene Ward Smith]]
Commas: 99/98, 176/175, 1029/1024
 
POTE generator: ~15/14 = 116.277
 
Map: [&lt;1 1 3 3 5|, &lt;0 6 -7 -2 -16|]
 
EDOs: {{EDOs|10e, 21, 31}}
 
Badness: 0.0329
 
=== 13-limit ===
Commas: 66/65, 99/98, 105/104, 512/507
 
POTE generator: ~15/14 = 116.268
 
Map: [&lt;1 1 3 3 5 4|, &lt;0 6 -7 -2 -16 -3|]
 
EDOs: {{EDOs|10e, 21, 31}}
 
Badness: 0.0295
 
== Hemimiracle ==
Commas: 225/224, 245/242, 1029/1024
 
POTE generator: ~33/32 = 58.408
 
Map: [&lt;1 1 3 3 4|, &lt;0 12 -14 -4 -11|]
 
EDOs: {{EDOs|20, 21, 41, 144e, 185cee, 226cee}}
 
Badness: 0.0592
 
=== 13-limit ===
Commas: 105/104, 196/195, 245/242, 512/507
 
POTE generator: ~33/32 = 58.430
 
Map: [&lt;1 1 3 3 4 4|, &lt;0 12 -14 -4 -11 -6|]
 
EDOs: {{EDOs|20, 21, 41, 144eff, 185ceeff}}
 
Badness: 0.0432
 
== Oracle ==
Commas: 121/120, 225/224, 1029/1024
 
POTE generator: ~11/8 = 541.668
 
Map: [&lt;1 7 -4 1 3|, &lt;0 -12 14 4 1|]
 
EDOs: {{EDOs|11, 20, 31, 51, 82e, 113e, 144ee}}


[http://www.archive.org/details/RachmaninoffPlaysBlackjack Rachmaninoff Plays Blackjack] [http://www.archive.org/download/RachmaninoffPlaysBlackjack/rachman.mp3 play]
Badness: 0.0427


By [[Joseph_Pehrson|Joseph Pehrson]]
== Music ==
By [[Gene Ward Smith]]


[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/blackandjill.mp3 Black and Jill]
* [http://www.archive.org/details/RachmaninoffPlaysBlackjack Rachmaninoff Plays Blackjack] [http://www.archive.org/download/RachmaninoffPlaysBlackjack/rachman.mp3 play]


[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/josephpehrson+blacklight.mp3 Blacklight]
By [[Joseph Pehrson]]


[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/josephpehrson+blackjack.mp3 Blackjack]
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/blackandjill.mp3 Black and Jill]
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/josephpehrson+blacklight.mp3 Blacklight]
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/josephpehrson+blackjack.mp3 Blackjack]


=Rodan=
= Rodan =
{{main|Rodan}}
{{main|Rodan}}
[[Comma|Commas]]: 245/243, 1029/1024
[[Comma|Commas]]: 245/243, 1029/1024
Line 273: Line 275:
Map: [&lt;1 1 -1 3|, &lt;0 3 17 -1|]
Map: [&lt;1 1 -1 3|, &lt;0 3 17 -1|]


EDOs: 5, 41, 87, 128, 215d
EDOs: {{EDOs|5, 41, 87, 128, 215d}}


Badness: 0.0371
Badness: 0.0371


==11-limit==
== 11-limit ==
[[Comma|Commas]]: 245/243, 385/384, 441/440
[[Comma|Commas]]: 245/243, 385/384, 441/440


Line 292: Line 294:
Map: [&lt;1 1 -1 3 6|, &lt;0 3 17 -1 -13|]
Map: [&lt;1 1 -1 3 6|, &lt;0 3 17 -1 -13|]


EDOs: 5, 41, 46, 87
EDOs: {{EDOs|5, 41, 46, 87}}


Badness: 0.0231
Badness: 0.0231


[[Chords_of_rodan|Chords of rodan]]
{{see also|Chords of rodan}}


==13-limit==
=== 13-limit ===
Commas: 196/195, 245/243, 352/351, 364/363
Commas: 196/195, 245/243, 352/351, 364/363


Line 317: Line 319:
Generators: 2, 8/7
Generators: 2, 8/7


EDOs: 41, 46, [[87edo|87]]
EDOs: {{EDOs|41, 46, 87}}


Badness: 0.0184
Badness: 0.0184


==17-limit==
==== 17-limit ====
Commas: 154/153, 196/195, 245/243, 256/255, 273/272
Commas: 154/153, 196/195, 245/243, 256/255, 273/272


Line 330: Line 332:
Map: [&lt;1 1 -1 3 6 8 8|, &lt;0 3 17 -1 -13 -22 -20|]
Map: [&lt;1 1 -1 3 6 8 8|, &lt;0 3 17 -1 -13 -22 -20|]


Edos: 41, 46, 87, 220dg, 307dgg
Edos: {{EDOs|41, 46, 87, 220dg, 307dgg}}


Badness: 0.0167
Badness: 0.0167


===Music===
=== Aerodactyl ===
By [[Gene_Ward_Smith|Gene Ward Smith]]
 
[http://www.archive.org/details/Pianodactyl Pianodactyl] [http://www.archive.org/download/Pianodactyl/pianodactyl.mp3 play]
 
==Aerodactyl==
Commas: 91/90, 245/243, 385/384, 441/440
Commas: 91/90, 245/243, 385/384, 441/440


Line 346: Line 343:
Map: [&lt;1 1 -1 3 6 -1|, &lt;0 3 17 -1 -13 24|
Map: [&lt;1 1 -1 3 6 -1|, &lt;0 3 17 -1 -13 24|


EDOs: 5, 41f, 46, 51c
EDOs: {{EDOs|5, 41f, 46, 51c}}


Badness: 0.0340
Badness: 0.0340


==Aerodino==
== Aerodino ==
Commas: 176/175, 245/243, 1029/1024
Commas: 176/175, 245/243, 1029/1024


Line 357: Line 354:
Map: [&lt;1 1 -1 3 -3|, &lt;0 3 17 -1 33|
Map: [&lt;1 1 -1 3 -3|, &lt;0 3 17 -1 33|


EDOS: 5e, 41e, 46
EDOS: {{EDOs|5e, 41e, 46}}


Badness: 0.0543
Badness: 0.0543


===13-limit===
=== 13-limit ===
Commas: 91/90, 176/175, 245/243, 847/845
Commas: 91/90, 176/175, 245/243, 847/845


Line 368: Line 365:
Map: [&lt;1 1 -1 3 -3 -1|, &lt;0 3 17 -1 33 24|
Map: [&lt;1 1 -1 3 -3 -1|, &lt;0 3 17 -1 33 24|


EDOs: 5e, 46
EDOs: {{EDOs|5e, 46}}


Badness: 0.0358
Badness: 0.0358


==Varan==
== Varan ==
Commas: 100/99, 245/243, 1029/1024
Commas: 100/99, 245/243, 1029/1024


Line 379: Line 376:
Map: [&lt;1 1 -1 3 -2|, &lt;0 3 17 -1 28|
Map: [&lt;1 1 -1 3 -2|, &lt;0 3 17 -1 28|


EDOs: 5e, 41, 46e
EDOs: {{EDOs|5e, 41, 46e}}


Badness: 0.0449
Badness: 0.0449


===13-limit===
=== 13-limit ===
Commas: 100/99, 105/104, 245/243, 352/351
Commas: 100/99, 105/104, 245/243, 352/351


Line 390: Line 387:
Map: [&lt;1 1 -1 3 -2 0|, &lt;0 3 17 -1 28 19|
Map: [&lt;1 1 -1 3 -2 0|, &lt;0 3 17 -1 28 19|


EDOs: 5e, 41
EDOs: {{EDOs|5e, 41}}


Badness: 0.0323
Badness: 0.0323
== Music ==
By [[Gene Ward Smith]]
* [http://www.archive.org/details/Pianodactyl Pianodactyl] [http://www.archive.org/download/Pianodactyl/pianodactyl.mp3 play]


= Valentine =
= Valentine =
Line 398: Line 400:
{{see also|Starling temperaments #Valentine}}
{{see also|Starling temperaments #Valentine}}


== 5-limit ==
Comma: 1990656/1953125
Comma: 1990656/1953125


Line 408: Line 411:
Badness: 0.1228
Badness: 0.1228


==7-limit==
== 7-limit ==
[[Comma|Commas]]: 126/125, 1029/1024
[[Comma]]s: 126/125, 1029/1024


[[Minimax_tuning|Minimax tuning]]:
[[Minimax tuning]]:


7-limit: [|1 0 0 0&gt;, |5/2 3/4 0 -3/4&gt;,
7-limit: [|1 0 0 0&gt;, |5/2 3/4 0 -3/4&gt;,
|17/6 5/12 0 -5/12&gt;, [5/2 -1/4 0 1/4&gt;<nowiki>]</nowiki>
|17/6 5/12 0 -5/12&gt;, [5/2 -1/4 0 1/4&gt;<nowiki>]</nowiki>


Eigenmonzos: 2, 7/6
[[Eigenmonzo]]s: 2, 7/6


9-limit: [|1 0 0 0&gt;, |10/7 6/7 0 -3/7&gt;,
9-limit: [|1 0 0 0&gt;, |10/7 6/7 0 -3/7&gt;,
|47/21 10/21 0 -5/21&gt;, |20/7 -2/7 0 1/7&gt;<nowiki>]</nowiki>
|47/21 10/21 0 -5/21&gt;, |20/7 -2/7 0 1/7&gt;<nowiki>]</nowiki>


Eigenmonzos: 2, 9/7
[[Eigenmonzo]]s: 2, 9/7


[[POTE_tuning|POTE generator]]: ~21/20 = 77.864
[[POTE_tuning|POTE generator]]: ~21/20 = 77.864


Algebraic generator: [[Algebraic_number|smaller root]] of x^2-89x+92, or (89-√7553)/2, at 77.8616 cents.
Algebraic generator: [[Algebraic_number|smaller root]] of x^2-89x+92, or (89-sqrt(7553))/2, at 77.8616 cents.


Map: [&lt;1 1 2 3|, &lt;0 9 5 -3|]
Map: [&lt;1 1 2 3|, &lt;0 9 5 -3|]


Wedgie: &lt;&lt;9 5 -3 -13 -30 -21||
Mapping [[generator]]s: 2, 21/20


EDOs: 15, 31, 46, 77, 185, 262cd
EDOs: {{EDOs|15, 31, 46, 77, 185, 262cd}}


Badness: 0.0311
Badness: 0.0311
Line 451: Line 454:
Map: [&lt;1 1 2 3 3|, &lt;0 9 5 -3 7|]
Map: [&lt;1 1 2 3 3|, &lt;0 9 5 -3 7|]


Generators: 2, 21/20
Mapping generators: 2, 21/20


[[EDO|EDOs]]: 15, 31, 46, 77, 262cdee, 339cdeee
[[EDO|EDOs]]: {{EDOs|15, 31, 46, 77, 262cdee, 339cdeee}}


Badness: 0.0167
Badness: 0.0167


[[Chords_of_valentine|Chords of valentine]]
{{see also|Chords of valentine}}


=Unidec=
= Unidec =
== 5-limit ==
Comma: 31381059609/31250000000
Comma: 31381059609/31250000000


Line 466: Line 470:
Map: [&lt;2 5 8|, &lt;0 -6 -11|]
Map: [&lt;2 5 8|, &lt;0 -6 -11|]


EDOs: 26, 46, 72, 118, 2524, 2642, 2760, 5002bc
EDOs: {{EDOs|26, 46, 72, 118, 2524, 2642, 2760, 5002bc}}


Badness: 0.0824
Badness: 0.0824
Line 491: Line 495:
Wedgie: &lt;&lt;12 22 -4 7 -40 -71||
Wedgie: &lt;&lt;12 22 -4 7 -40 -71||


EDOs: 26, 46, 72, 118, 190
EDOs: {{EDOs|26, 46, 72, 118, 190}}


Badness: 0.0384
Badness: 0.0384
Line 505: Line 509:
[[Eigenmonzo|Eigenmonzos]]: 2, 9/7
[[Eigenmonzo|Eigenmonzos]]: 2, 9/7


[[POTE_tuning|POTE generator]]: 183.165
[[POTE_tuning|POTE generator]]: ~10/9 = 183.165


Map: [&lt;2 5 8 5 6|, &lt;0 -6 -11 2 3|]
Map: [&lt;2 5 8 5 6|, &lt;0 -6 -11 2 3|]


EDOs: 26, 46, 72, 118, 190
EDOs: {{EDOs|26, 46, 72, 118, 190}}


Badness: 0.0155
Badness: 0.0155
Line 515: Line 519:
[[Chords_of_unidec|Chords of unidec]]
[[Chords_of_unidec|Chords of unidec]]


==Ekadash==
=== Ekadash ===
Commas: 385/384, 441/440, 625/624, 729/728
Commas: 385/384, 441/440, 625/624, 729/728


Line 522: Line 526:
Map: [&lt;2 5 8 5 6 19|, &lt;0 -6 -11 2 3 -38|]
Map: [&lt;2 5 8 5 6 19|, &lt;0 -6 -11 2 3 -38|]


EDOs: 20cf, 26f, 46f, 72, 118, 190, 262df, 452cdef
EDOs: {{EDOs|20cf, 26f, 46f, 72, 118, 190, 262df, 452cdef}}


Badness: 0.0204
Badness: 0.0204


==Hendec==
=== Hendec ===
Commas: 169/168, 325/324, 364/363, 1716/1715
Commas: 169/168, 325/324, 364/363, 1716/1715


Line 533: Line 537:
Map: [&lt;2 5 8 5 6 8|, &lt;0 -6 -11 2 3 -2|]
Map: [&lt;2 5 8 5 6 8|, &lt;0 -6 -11 2 3 -2|]


EDOs: 26, 46, 72
EDOs: {{EDOs|26, 46, 72}}


Badness: 0.0177
Badness: 0.0177


===17-limit===
==== 17-limit ====
Commas: 169/168, 221/220, 273/272, 325/324, 364/363
Commas: 169/168, 221/220, 273/272, 325/324, 364/363


Line 546: Line 550:
EDOs: 26, 46, 72
EDOs: 26, 46, 72


===Music===
== Music ==
[[Technical_Notes_for_Newbeams#Track notes:-Hypnocloudsmack 2|Hypnocloudsmack 2]] by [[Andrew_Heathwaite|Andrew Heathwaite]]
[[Technical_Notes_for_Newbeams#Track notes:-Hypnocloudsmack 2|Hypnocloudsmack 2]] by [[Andrew Heathwaite]]


= Hemithirds =
= Hemithirds =
Line 607: Line 611:
Badness: 0.0217
Badness: 0.0217


=Hemiseven=
= Hemiseven =
 
==7-limit==
Commas: 1029/1024, 19683/19600
Commas: 1029/1024, 19683/19600


Line 618: Line 620:
Wedgie: &lt;&lt;6 29 -2 32 -20 -86||
Wedgie: &lt;&lt;6 29 -2 32 -20 -86||


EDOs: 5, 72, 77, 149, 221, 514bd, 735bcd
EDOs: {{EDOs|5, 72, 77, 149, 221, 514bd, 735bcd}}


Badness: 0.0566
Badness: 0.0566


==11-limit==
== 11-limit ==
Commas: 385/384, 441/440, 19683/19600
Commas: 385/384, 441/440, 19683/19600


Line 629: Line 631:
Map: [&lt;1 4 14 2 -5|, &lt;0 -6 -29 2 21|]
Map: [&lt;1 4 14 2 -5|, &lt;0 -6 -29 2 21|]


EDOs: 72, 77, 149, 221e, 293de
EDOs: {{EDOs|72, 77, 149, 221e, 293de}}


Badness: 0.0285
Badness: 0.0285


==13-limit==
== 13-limit ==
Commas: 351/350, 385/384, 441/440, 676/675
Commas: 351/350, 385/384, 441/440, 676/675


Line 640: Line 642:
Map: [&lt;1 4 14 2 -5 19|, &lt;0 -6 -29 2 21 -38|]
Map: [&lt;1 4 14 2 -5 19|, &lt;0 -6 -29 2 21 -38|]


EDOs: 72, 77, 149, 221ef
EDOs: {{EDOs|72, 77, 149, 221ef}}


==17-limit==
== 17-limit ==
Commas: 273/272, 351/350, 385/384, 441/440, 676/675
Commas: 273/272, 351/350, 385/384, 441/440, 676/675


Line 649: Line 651:
Map: [&lt;1 4 14 2 -5 19 21|, &lt;0 -6 -29 2 21 -38 -42|]
Map: [&lt;1 4 14 2 -5 19 21|, &lt;0 -6 -29 2 21 -38 -42|]


EDOs: 72, 77, 149, 221ef
EDOs: {{EDOs|72, 77, 149, 221ef}}


=Tritikleismic=
= Tritikleismic =
{{see also|Kleismic family #Tritikleismic}}


==7-limit==
== 7-limit ==
[[Comma|Commas]]: 1029/1024, 15625/15552
[[Comma|Commas]]: 1029/1024, 15625/15552


Line 672: Line 675:
Map: [&lt;3 0 3 10|, &lt;0 6 5 -2|]
Map: [&lt;3 0 3 10|, &lt;0 6 5 -2|]


[[EDO|EDOs]]: [[15edo|15]], [[72edo|72]], [[87edo|87]], [[159edo|159]], [[231edo|231]]
[[EDO|EDOs]]: {{EDOs|15, 72, 87, 159, 231}}


Badness: 0.0563
Badness: 0.0563


==11-limit==
== 11-limit ==
[[Comma|Commas]]: 385/384, 441/440, 4000/3993
[[Comma|Commas]]: 385/384, 441/440, 4000/3993


Line 690: Line 693:
Map: [&lt;3 0 3 10 8|, &lt;0 6 5 -2 3|]
Map: [&lt;3 0 3 10 8|, &lt;0 6 5 -2 3|]


EDOs: 72, 159, 231
EDOs: {{EDOs|72, 159, 231}}


Badness: 0.0193
Badness: 0.0193


==13-limit==
== 13-limit ==
Commas: 325/324, 364/363, 441/440, 625/624
Commas: 325/324, 364/363, 441/440, 625/624


Map: [&lt;3 0 3 10 8 0|, &lt;0 6 5 -2 3 14|]
Map: [&lt;3 0 3 10 8 0|, &lt;0 6 5 -2 3 14|]


EDOs: 15, 72, 87, 159
EDOs: {{EDOs|15, 72, 87, 159}}


==17-limit==
== 17-limit ==
Commas: 273/272, 325/324, 364/363, 375/374, 385/384
Commas: 273/272, 325/324, 364/363, 375/374, 385/384


Map: [&lt;3 0 3 10 8 0 -2|, &lt;0 6 5 -2 3 14 18|]
Map: [&lt;3 0 3 10 8 0 -2|, &lt;0 6 5 -2 3 14 18|]


EDOs: 15g, 72, 87, 159
EDOs: {{EDOs|15g, 72, 87, 159}}


=Superkleismic=
= Superkleismic =
Commas: 1029/1024, 875/864
Commas: 1029/1024, 875/864


Line 715: Line 718:
Map: [&lt;1 4 5 2|, &lt;0 -9 -10 3|]
Map: [&lt;1 4 5 2|, &lt;0 -9 -10 3|]


EDOs: 11, 15, 26, 41
EDOs: {{EDOs|11, 15, 26, 41}}


Badness: 0.0479
Badness: 0.0479


==11-limit==
== 11-limit ==
Commas: 100/99, 245/242, 385/384
Commas: 100/99, 245/242, 385/384


Line 726: Line 729:
Map: [&lt;1 4 5 2 4|, &lt;0 -9 -10 3 -2|]
Map: [&lt;1 4 5 2 4|, &lt;0 -9 -10 3 -2|]


EDOs: 15, 26, 41, 261
EDOs: {{EDOs|15, 26, 41, 261}}


Badness: 0.0257
Badness: 0.0257


==13-limit==
== 13-limit ==
Commas: 100/99, 105/104, 245/243, 1188/1183
Commas: 100/99, 105/104, 245/243, 1188/1183


Line 737: Line 740:
Map: [&lt;1 4 5 2 4 8|, &lt;0 -9 -10 3 -2 -16|]
Map: [&lt;1 4 5 2 4 8|, &lt;0 -9 -10 3 -2 -16|]


EDOs: 11, 15, 26, 41
EDOs: {{EDOs|11, 15, 26, 41}}


Badness: 0.0215
Badness: 0.0215


=Gorgo=
= Gorgo =
Commas: 36/35, 1029/1024
Commas: 36/35, 1029/1024


Line 750: Line 753:
Wedgie: &lt;&lt;3 7 -1 4 -10 -22||
Wedgie: &lt;&lt;3 7 -1 4 -10 -22||


EDOs: 5, 16, 21
EDOs: {{EDOs|5, 16, 21}}


Badness: 0.0607
Badness: 0.0607


==11-limit==
== 11-limit ==
Commas: 36/35, 56/55, 1029/1024
Commas: 36/35, 56/55, 1029/1024


Line 761: Line 764:
Map: [&lt;1 1 1 3 5|, &lt;0 3 7 -1 -8|]
Map: [&lt;1 1 1 3 5|, &lt;0 3 7 -1 -8|]


EDOs: 5, 16e, 21, 47c, 68bce
EDOs: {{EDOs|5, 16e, 21, 47c, 68bce}}


Badness: 0.0627
Badness: 0.0627


==13-limit==
== 13-limit ==
Commas: 27/26, 36/35, 56/55, 507/500
Commas: 27/26, 36/35, 56/55, 507/500


Line 772: Line 775:
Map: [&lt;1 1 1 3 5 2|, &lt;0 3 7 -1 -8 9|]
Map: [&lt;1 1 1 3 5 2|, &lt;0 3 7 -1 -8 9|]


EDOs 5, 21, 68bcef
EDOs {{EDOs|5, 21, 68bcef}}


Badness: 0.0471
Badness: 0.0471


==Music==
==Music==
[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/gorgo-example.mp3 Gorgo Example] by [[Herman_Miller|Herman Miller]]
[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/gorgo-example.mp3 Gorgo Example] by [[Herman Miller]]
 
= Lemba =
{{see also|Jubilismic clan #Lemba}}


=Lemba=
Commas: 50/49, 525/512
Commas: 50/49, 525/512


Line 788: Line 793:
Wedgie: &lt;&lt;6 -2 -2 -17 -20 1||
Wedgie: &lt;&lt;6 -2 -2 -17 -20 1||


EDOs: 10, 16, 26
EDOs: {{EDOs|10, 16, 26}}


Badness: 0.0622
Badness: 0.0622
Line 795: Line 800:
By [[Herman_Miller|Herman Miller]]
By [[Herman_Miller|Herman Miller]]


[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/LembaGalatsia.mp3 Lemba Galatsia]
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/LembaGalatsia.mp3 Lemba Galatsia]
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/lemba-gpo-test.mp3 GPO Lemba]


[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/lemba-gpo-test.mp3 GPO Lemba]
= Gidorah =
 
{{see also|University temperament}}
=Gidorah=


Commas: 21/20, 144/125
Commas: 21/20, 144/125
Line 807: Line 812:
Map: [&lt;1 1 2 3|, &lt;0 3 2 -1|]
Map: [&lt;1 1 2 3|, &lt;0 3 2 -1|]


EDOs: 5, 11, 16c, 21cc, 26ccc
EDOs: {{EDOs|5, 11, 16c, 21cc, 26ccc}}


Badness: 0.0623
Badness: 0.0623


: ''see also [[University temperament]]''
= Clyndro =
 
=Clyndro=
Commas: 135/128, 360/343
Commas: 135/128, 360/343


Line 820: Line 823:
Map: [&lt;1 1 4 3|, &lt;0 3 -9 -1|]
Map: [&lt;1 1 4 3|, &lt;0 3 -9 -1|]


EDOs: 5c, 11, 16
EDOs: {{EDOs|5c, 11, 16}}


Badness: 0.1592
Badness: 0.1592


==11-limit==
== 11-limit ==
Commas: 33/32, 45/44, 352/343
Commas: 33/32, 45/44, 352/343


Line 831: Line 834:
Map: [&lt;1 1 4 3 4|, &lt;0 3 -9 -1 -3|]
Map: [&lt;1 1 4 3 4|, &lt;0 3 -9 -1 -3|]


EDOs: 5c, 11, 16
EDOs: {{EDOs|5c, 11, 16}}


Badness: 0.0697
Badness: 0.0697


=Necromanteion=
= Necromanteion =
Commas: 1029/1024, 5103/5000
Commas: 1029/1024, 5103/5000


Line 842: Line 845:
Map: [&lt;1 7 10 1|, &lt;0 -12 -17 4|]
Map: [&lt;1 7 10 1|, &lt;0 -12 -17 4|]


EDOs: 11c, 20c, 31, 51c, 82c, 113c, 144c, 175c, 206bc, 237bc, 505bcd
EDOs: {{EDOs|11c, 20c, 31, 51c, 82c, 113c, 144c, 175c, 206bc, 237bc, 505bcd}}


Badness: 0.1177
Badness: 0.1177


==11-limit==
== 11-limit ==
Commas: 176/175, 243/242, 1029/1024
Commas: 176/175, 243/242, 1029/1024


Line 853: Line 856:
Map: [&lt;1 7 10 1 17|, &lt;0 -12 -17 4 -30|]
Map: [&lt;1 7 10 1 17|, &lt;0 -12 -17 4 -30|]


EDOs: 31, 82c, 113c, 144c, 175c, 350bcde, 381bcde
EDOs: {{EDOs|31, 82c, 113c, 144c, 175c, 350bcde, 381bcde}}


Badness: 0.0535
Badness: 0.0535


==13-limit==
== 13-limit ==
Commas: 144/143, 176/175, 243/242, 343/338
Commas: 144/143, 176/175, 243/242, 343/338


Line 864: Line 867:
Map: [&lt;1 7 10 1 17 1|, &lt;0 -12 -17 4 -30 6|]
Map: [&lt;1 7 10 1 17 1|, &lt;0 -12 -17 4 -30 6|]


EDOs: 31, 51ce, 82cf, 113cf, 144cf
EDOs: {{EDOs|31, 51ce, 82cf, 113cf, 144cf}}


Badness: 0.0470
Badness: 0.0470


=Widefourth=
= Widefourth =
Commas: 1029/1024, 48828125/48771072
Commas: 1029/1024, 48828125/48771072


Line 877: Line 880:
Wedgie: &lt;&lt;33 13 -11 -56 -110 -62||
Wedgie: &lt;&lt;33 13 -11 -56 -110 -62||


EDOs: 16, 71, 87, 103, 190
EDOs: {{EDOs|16, 71, 87, 103, 190}}


Badness: 0.1541
Badness: 0.1541


==11-limit==
== 11-limit ==
Commas: 385/384, 441/440, 234375/234256
Commas: 385/384, 441/440, 234375/234256


Line 888: Line 891:
Map: [&lt;1 16 8 -2 17|, &lt;0 -33 -13 11 -31|]
Map: [&lt;1 16 8 -2 17|, &lt;0 -33 -13 11 -31|]


EDOs: 16, 71, 87, 103, 190
EDOs: {{EDOs|16, 71, 87, 103, 190}}


Badness: 0.0408
Badness: 0.0408


==13-limit==
== 13-limit ==
Commas: 385/384, 441/440, 625/624, 847/845
Commas: 385/384, 441/440, 625/624, 847/845


Line 899: Line 902:
Map: [&lt;1 16 8 -2 17 12|, &lt;0 -33 -13 11 -31 -19|]
Map: [&lt;1 16 8 -2 17 12|, &lt;0 -33 -13 11 -31 -19|]


EDOs: 16, 71, 87, 103, 190
EDOs: {{EDOs|16, 71, 87, 103, 190}}


Badness: 0.0216
Badness: 0.0216


=Tritriple=
= Tritriple =
== 5-limit ==
Comma: |31 20 -27&gt;
Comma: |31 20 -27&gt;


Line 910: Line 914:
Map: [&lt;1 -11 -7|, &lt;0 27 20|]
Map: [&lt;1 -11 -7|, &lt;0 27 20|]


EDOs: 15, 103, 118, 133, 959, 1077
EDOs: {{EDOs|15, 103, 118, 133, 959, 1077}}


Badness: 0.2836
Badness: 0.2836


==7-limit==
== 7-limit ==
Commas: 1029/1024, 1959552/1953125
Commas: 1029/1024, 1959552/1953125


Line 921: Line 925:
Map: [&lt;1 -11 -7 7|, &lt;0 27 20 -9|]
Map: [&lt;1 -11 -7 7|, &lt;0 27 20 -9|]


EDOs: 15, 103, 118, 133, 339d
EDOs: {{EDOs|15, 103, 118, 133, 339d}}


Badness: 0.1186
Badness: 0.1186


==11-limit==
== 11-limit ==
Commas: 385/384, 441/440, 43923/43750
Commas: 385/384, 441/440, 43923/43750


Line 932: Line 936:
Map: [&lt;1 -11 -7 7 -4|, &lt;0 27 20 -9 16|]
Map: [&lt;1 -11 -7 7 -4|, &lt;0 27 20 -9 16|]


EDOs: 15, 103, 118, 133, 339de
EDOs: {{EDOs|15, 103, 118, 133, 339de}}


Badness: 0.0353
Badness: 0.0353
Line 943: Line 947:
Map: [<1 -2 8 4|, <0 12 -19 -4|]
Map: [<1 -2 8 4|, <0 12 -19 -4|]


EDOs: 10, 67, 77, 87, 164
EDOs: {{EDOs|10, 67, 77, 87, 164}}


Badness: 0.1080
Badness: 0.1080
Line 954: Line 958:
Map: [<1 -2 8 4 -7|, <0 12 -19 -4 35|]
Map: [<1 -2 8 4 -7|, <0 12 -19 -4 35|]


EDOs: 10, 77, 87, 164
EDOs: {{EDOs|10, 77, 87, 164}}


Badness: 0.0547
Badness: 0.0547
Line 965: Line 969:
Map: [<1 -2 8 4 -7 4|, <0 12 -19 -4 35 -1|]
Map: [<1 -2 8 4 -7 4|, <0 12 -19 -4 35 -1|]


EDOs: 10, 77, 87, 164
EDOs: {{EDOs|10, 77, 87, 164}}


Badness: 0.0282
Badness: 0.0282
=Baladic=
=Baladic=
Baladic is a 2.3.7.13.17 subgroup temperament that attempts to approximate the Maqam Sikah Baladi scale. 36edo is an excellent baladic tuning.
Baladic is a 2.3.7.13.17 subgroup temperament that attempts to approximate the Maqam Sikah Baladi scale. 36edo is an excellent baladic tuning.
Line 979: Line 984:
Map: [<2 2 6 7 7|, <0 3 -1 1 3|]
Map: [<2 2 6 7 7|, <0 3 -1 1 3|]


EDOs: 26, 36, 46, 82, 118f
EDOs: {{EDOs|26, 36, 46, 82, 118f}}
 


[[Category:Theory]]
[[Category:Theory]]
Line 986: Line 990:
[[Category:Clan]]
[[Category:Clan]]
[[Category:Miracle]]
[[Category:Miracle]]
[[Category:Rodan]]
[[Category:Rank 2]]
[[Category:Listen]]
[[Category:Listen]]


[[Category:Todo:improve layout]]
[[Category:Todo:review]]
[[Category:Todo:review]]
Retrieved from "https://en.xen.wiki/w/Gamelismic_clan"